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Effective learning methods advice

  1. May 31, 2013 #1
    Hello all,

    I have began my informal study of mathematics (online non-assessed) and i have a few questions..

    I currently study for 1 hour per day 6 days per week however i will be increasing that to 2 hours come Monday. Before embarking on this journey i decided that i was going to do a complete refresher and fill in any gaps that there may be in my knowledge, so i started from addition and am currently working through factors and multiples. I hope to take this through all the way to calculus, linear algebra and differential equations etc..

    The reason for all of this study is that i need to complete some prerequisite study which is basically high school level methods mathematics and physics (senior mathematics through unilearn). I am doing this because i want to get into a science degree.

    First question: would it be advisable to study for more than 4 hours per day (causing me to possibly learn multiple topics in a close space of time ie. from fractions to ratios to scientific notation all really quickly? Or would this be ineffective and cause me to retain less of the information due to becoming overloaded with too many different concepts?

    I guess that was my only question :tongue: i ask it because i need to get my understanding to at least trigonometry and maybe even some calculus before beginning this prerequisite study and i would very much like the dates to line up so that i can begin my formal education ASAP
     
  2. jcsd
  3. May 31, 2013 #2
    One way you can make sure you actually remember everything you study when you spend a lot of time on it is to spend more time on the same subjects. If you double your study time, then double your time on each subject, don't learn twice as many subjects.

    4 hours a day is definitely doable. Doesn't mean you have to, but you could. What I think you should do with your extra time is think about WHY the thing you just learned is the way it is. For example, in algebra you are told to do the same thing to both sides of the equation. Why is that? Sometimes you won't know the answer, and there's no shame in that. I think math is a lot more enjoyable and easier when you understand why it's the way it is. Another example: scientific notation is obvious if you understand decimals, exponents, and multiplication very well. It's just an expression that multiplies out to the number you are talking about. So when you learn it, think about what kinds of numbers would be best described using scientific notation.
     
  4. May 31, 2013 #3
    solid advice DIM i completely agree as i want to actually learn this stuff and form a stable foundation for my further studies. However i have these dates looming and i am experiencing some concern about pushing back the date at which my formal education starts (i understand that it is no more valid than the informal learning in the grand scheme of things but i think you can understand my nervousness regarding it..)

    Do you think it would be forgiven if i were to begin the formal studies (senior math) before having reached these concepts in my informal study?

    Senior math:
    -functions and their graphs
    -coordinate geometry
    -trigonometry and periodic functions
    -an introduction to differential and integral calculus
    -statistics and probability.

    It would begin immediately along with a physics course that would run for the same amount of time (no longer than 6 months) upon completion of these i would apply for semester 1 bachelor of science at my second choice university and then transfer into my first choice in semester 2

    option 2 is to get the foundation down (informal study in math) then once that has been completed (i assume it would take a few months to get to the point where i am at "calculus level") begin the senior math course and then take a different physics foundation course offered through my first choice university that includes a lab component in the study in semester 1 and finally apply for semester 2 entry into the bachelor of science.
    iv also been told that semester 2 applications are more competitive so that adds to my NERVOUSNESS!!!! :O
     
    Last edited: May 31, 2013
  5. May 31, 2013 #4

    Stephen Tashi

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    Science Advisor

    Judging when you understand something is a big problem for people who are self taught. On the one hand, you may think you understand something and end up having a complete misconception of it. On the other hand, you can spend hours perfecting your knowledge of some particular kind of problem until you can work such problems in your sleep, but be slowed down so much that you never complete your studies.

    Everyone has gaps in their knowledge. Your goal, if you want an academic degree, should be to have about the same gaps and fills that the other degree students have. So it will be useful to discuss the material you study with other people by posting specific questions on the forum or attempting to answer specific questions. (Your recent posts haven't been very specific..) It will be helpful to give yourself tests and exams that objectively measure how well you know a topic. I don't think that its necessary for you to study a topic until you make 100% on a test about it. You should make a passing mark.

    The other posters make a distinction between knowing a topic and drilling yourself in it. This is a useful thing to keep in mind. There is a difference between understanding a topic well enough to eventually figure out a problem and being so familiar with that type of problem that you can do it rapidly. If you are in an academic course, you'll want to have drilled on the same type of problems that the other students have dilled. The number of times that textbooks give a certain type of problem as an exercise is good indication of how much students are expected to drill at it.

    There are a few people that can make time budgets for study, make lists of books, make outlines of topics etc. and actually carry out a program of study. It's more common to see people make such elaborate plans as an expression of ambition and then never carry out the program. Don't spend too much of your time planning a program of study. Planning can turn into a form of daydreaming. Daydreaming is useful for the purposes of motivation, but it can be so entertaining that it crowds out the actual execution of the plan.
     
  6. May 31, 2013 #5
    Curiosity about the subject might not be enough to actually learn the subject, because curiosity, by its nature, sidetracks you, a lot. At the end of the day, you might feel all those small bits you learned here and there don't add up to anything, as opposed to, for example, a chapter or a passed exam.
    That's why I feel it's important to have some easy to grasp, almost slogan-like goal. There might be many arguments against university education, but, unless you keep a clear goal in mind, this is a strong argument against self-study.
    Anyway, that's my experience, I might have ADHD. *irony*
     
  7. May 31, 2013 #6

    verty

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    Homework Helper

    This sounds prohibitively difficult to me. To learn by yourself 11 or so years of school math may not be possible. If it is at all possible, it could only be done in a progressive manner, something like this perhaps:

    Level 1 - arithmetic
    Level 2 - algebra: equations and inequalities
    Level 3 - synthetic geometry
    Level 4 - coordinate geometry
    Level 5 - the rest of school algebra
    Level 6 - trigonometry

    Some order like this, where you only move to the next level when your knowledge up to the current level is complete and verified. By verified I mean, everything that schools teach, you know.
     
  8. Jun 3, 2013 #7
    Yes verty that is what i think il be doing instead of trying to rush ahead to meet some dates.. I think rushing for a deadline will cause me stress which will in-turn negatively impact my knowledge retention and also cause me to make some bad stress/anxiety driven decisions..

    It looks like (not confirmed) i will be beginning my prerequisite study later on this year and completing it in may of 2014 just in time for me to apply for semester 2 entry. This will give me a few months (may still be cutting this close) to refresh/learn the following:

    -Arithmetic and pre algebra (i am currently learning divisibility and and prime factorization)
    -Algebra
    -Geometry
    -Trigonometry and pre calculus

    after having learnt this i think i will be ready to begin my math prerequisite which involves:
    -functions and their graphs
    -coordinate geometry
    -trigonometry and periodic functions
    -an introduction to differential and integral calculus
    -statistics and probability.

    what do you guys think?
     
  9. Jun 3, 2013 #8

    verty

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    Homework Helper

    Just do as much as you can. Hopefully that prerequisites course will help to fill in any gaps, and if you've seen the stuff before, it'll go easier and be more fulfilling.
     
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